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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Scattering of a sound wave by a two-sided sandwich
membrane - Yuri Antipov (Louisiana State Universi
ty)
DTSTART;TZID=Europe/London:20230210T114500
DTEND;TZID=Europe/London:20230210T123000
UID:TALK194842AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194842
DESCRIPTION:Scattering of a sound plane wave by an infinite th
in structure is considered. The structure is compo
sed of a semi-infinite two-sided sandwich membrane
perforated on one side and a semi-infinite acoust
ically hard screen. On the perforated and continuo
us sides\, the velocity potential satisfies the fi
rst order Leppington and third order membrane boun
dary conditions\, respectively. Two ways of applyi
ng the Fourier transforms to the boundary value pr
oblem lead to distinct governing systems of two Wi
ener-Hopf functional equations. It is shown that b
oth Wiener-Hopf problems share the same characteri
stic polynomial and elliptic surface but reduce to
different genus-1 scalar Riemann-Hilbert problems
. The associated Jacobi inversion problem is solve
d in terms of \;the genus-1 Riemann theta func
tion. Exact formulas for the Wiener-Hopf matrix fa
ctors are presented. The solvability of the proble
m and the discontinuity of the solution at the scr
eens junction are discussed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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